Spectrality

Abstract

In the last chapter we saw how Gleason’s theorem provided us with out first connection between physical observables and Hermitian operators. Beginning with a Hilbert space H and its projection logic, we defined an observable as a logic-valued function on the real Borel sets. Then through expected values every observable was shown to be associated with a member of M ^*_σ (H), and then every member of M ^*_σ (H) was associated with a Hermitian operator on H by Gleason’s theorem and the spectral theorem.